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Capture recapture

Free Printable Capture recapture PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 6)

Download free capture recapture worksheets (PDF), GCSE maths past paper questions and worked solutions for Capture recapture (6P). This is a Grade 6 statistics topic from the GCSE questions by topic collection for Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, 1st Class Maths, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our capture recapture revision notes and worked examples with diagrams, try real GCSE past paper capture recapture questions with step-by-step solutions, or download a PDF of all capture recapture worksheet links.

Free Capture recapture PDF Worksheets & Answers

Grade 6 • Topic 6P
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
 Qs Ans
Textbook Exercise & answers
 Qs Ans
Edexcel exam questions & solutions
 Qs Ans
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
Self-marking online worksheet
 Page
Grade 6 topics
6A - Recurring decimals6B - Harder indices
6C - The product rule6D - Repeated change
6E - Triple brackets6F - Parallel and perpendicular
6G - Inequalities on graphs6H - Similar shapes (area and vol)
6J - Negative scale factors6K - Circle theorems
6L - Cumulative frequency6M - Box plots
6N - Combined transformations6P - Capture recapture
GCSE Maths Grade 6 Revision Notes & Method

Guide to Capture recapture: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Capture-recapture estimates a total population size N. First, M animals are caught, marked, and released. Later, a second sample of n animals is caught and m of them are found to have marks. Assuming the marked animals mixed randomly, equate the two proportions: MN = mn → N = M × nm.

Key assumptions: no births, deaths, or migration between samples; marks do not rub off; and every animal has an equal chance of being caught.

Example 1: A scientist catches 40 fish in a lake, marks them, and releases them. Next day she catches 60 fish and finds 8 are marked. Estimate the total fish population.

Solution:

Set up equal proportions: 40N = 860
Rearrange for N: N = 40 × 608
N = 2400 ÷ 8 = 300
Answer: 300 fish

Example 2: How would the estimate in Example 1 be affected if some of the marks had washed off overnight?

Solution:

Fewer marked fish (a smaller denominator m) would be recorded in the second sample.
Dividing 40 × 60 by a smaller number gives a larger result:
Answer: The population estimate would be too high (an overestimate).
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Capture recapture Questions & Answers

Past Paper Example 1 Eduqas Jun 2017 1H Q3 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The scale drawing below shows a lake.
There are two small islands in the lake at A and B.
The lifeguard station is marked at C.
ABCLakeShore
Swimming is only allowed in the area of the lake that is,
• nearer to A than it is to B and
• less than 60 metres from C.
Using a ruler and a pair of compasses, show accurately on the diagram the area where swimming is allowed.
Shade the area where swimming is allowed.
Use the scale 1 cm represents 10 m.
Worked Solution & Mark Scheme (4 marks)
1. Construct perpendicular bisector of AB with compass arcs. M2
2. Draw arc of radius 6 cm from center C. M1
3. Identify and shade the region inside the lake on A's side of the bisector and inside the circle from C. A1
Answer: Region bounded inside the lake by the perpendicular bisector of line segment AB (closer to A) and within an arc of radius 6 cm centered at C, correctly shaded.
Past Paper Example 2 GCSE Nov 2022 2H Q15 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
Faiza is studying the population of rabbits in a park.
She wants to estimate the number of rabbits in the park.
On Monday she catches a random sample of 20 rabbits in the park, marks each rabbit with a tag and releases them back into the park.
On Tuesday she catches a random sample of 42 rabbits in the park.
12 of the rabbits are marked with a tag.
(a) Find an estimate for the number of rabbits in the park. [3 marks]
(b) Explain why Albie’s estimate cannot be correct. [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
20 / N = 12 / 42 M2
⇒ N = (20 × 42) ÷ 12 = 70 A1
Answer (a): 70
Part (b) Solution:
He caught 55 rabbits, so there must be at least 55 rabbits in the wood (the sample size cannot be greater than the population)
Answer (b): He caught 55 rabbits, so there must be at least 55 rabbits in the wood (the sample size cannot be greater than the population)
Past Paper Example 3 GCSE Nov 2024 3H Q18 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
Maria wants to find an estimate for the number of frogs in a lake.
On Saturday she catches 40 of the frogs.
She puts a tag on each frog and releases them.
On Monday she catches 55 of the frogs.
11 of the frogs have tags.
(a) Work out an estimate for the total number of frogs in the lake.
You must show all your working. [3 marks]
(b) State one assumption you have made. [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
40 / N = 11 / 55 = 1 / 5 M2
⇒ N = 40 × 5 = 200 A1
Answer (a): 200
Part (b) Solution:
No frogs entered or left the lake (or no tags fell off, and the tagged frogs mixed thoroughly)
Answer (b): No frogs entered or left the lake (or no tags fell off, and the tagged frogs mixed thoroughly)

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